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Lógica matemática/ BD+BA+AC̅+BC

Expresión BD+BA+AC̅+BC

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

    Ha introducido [src] 
    (b∧c)∨(¬((a∧b)∨(a∧c)∨(b∧d)))
    $$\left(b \wedge c\right) \vee \neg \left(\left(a \wedge b\right) \vee \left(a \wedge c\right) \vee \left(b \wedge d\right)\right)$$
    Solución detallada
    $$\neg \left(\left(a \wedge b\right) \vee \left(a \wedge c\right) \vee \left(b \wedge d\right)\right) = \left(\neg a \wedge \neg b\right) \vee \left(\neg a \wedge \neg d\right) \vee \left(\neg b \wedge \neg c\right)$$
    $$\left(b \wedge c\right) \vee \neg \left(\left(a \wedge b\right) \vee \left(a \wedge c\right) \vee \left(b \wedge d\right)\right) = \left(b \wedge c\right) \vee \left(\neg a \wedge \neg b\right) \vee \left(\neg a \wedge \neg d\right) \vee \left(\neg b \wedge \neg c\right)$$
    Simplificación [src]
    $$\left(b \wedge c\right) \vee \left(\neg a \wedge \neg b\right) \vee \left(\neg a \wedge \neg d\right) \vee \left(\neg b \wedge \neg c\right)$$ 
    (b∧c)∨((¬a)∧(¬b))∨((¬a)∧(¬d))∨((¬b)∧(¬c))
    Tabla de verdad 
    +---+---+---+---+--------+
| a | b | c | d | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
    FNC [src]
    $$\left(b \vee \neg a \vee \neg b\right) \wedge \left(b \vee \neg a \vee \neg c\right) \wedge \left(b \vee \neg b \vee \neg d\right) \wedge \left(c \vee \neg a \vee \neg b\right) \wedge \left(c \vee \neg a \vee \neg c\right) \wedge \left(c \vee \neg b \vee \neg d\right) \wedge \left(b \vee \neg a \vee \neg b \vee \neg c\right) \wedge \left(b \vee \neg a \vee \neg b \vee \neg d\right) \wedge \left(b \vee \neg a \vee \neg c \vee \neg d\right) \wedge \left(b \vee \neg b \vee \neg c \vee \neg d\right) \wedge \left(c \vee \neg a \vee \neg b \vee \neg c\right) \wedge \left(c \vee \neg a \vee \neg b \vee \neg d\right) \wedge \left(c \vee \neg a \vee \neg c \vee \neg d\right) \wedge \left(c \vee \neg b \vee \neg c \vee \neg d\right)$$ 
    (b∨(¬a)∨(¬b))∧(b∨(¬a)∨(¬c))∧(b∨(¬b)∨(¬d))∧(c∨(¬a)∨(¬b))∧(c∨(¬a)∨(¬c))∧(c∨(¬b)∨(¬d))∧(b∨(¬a)∨(¬b)∨(¬c))∧(b∨(¬a)∨(¬b)∨(¬d))∧(b∨(¬a)∨(¬c)∨(¬d))∧(b∨(¬b)∨(¬c)∨(¬d))∧(c∨(¬a)∨(¬b)∨(¬c))∧(c∨(¬a)∨(¬b)∨(¬d))∧(c∨(¬a)∨(¬c)∨(¬d))∧(c∨(¬b)∨(¬c)∨(¬d))
    FND [src]
    Ya está reducido a FND
    $$\left(b \wedge c\right) \vee \left(\neg a \wedge \neg b\right) \vee \left(\neg a \wedge \neg d\right) \vee \left(\neg b \wedge \neg c\right)$$ 
    (b∧c)∨((¬a)∧(¬b))∨((¬a)∧(¬d))∨((¬b)∧(¬c))
    FNDP [src]
    $$\left(b \wedge c\right) \vee \left(\neg a \wedge \neg b\right) \vee \left(\neg a \wedge \neg d\right) \vee \left(\neg b \wedge \neg c\right)$$ 
    (b∧c)∨((¬a)∧(¬b))∨((¬a)∧(¬d))∨((¬b)∧(¬c))
    FNCD [src]
    $$\left(b \vee \neg a \vee \neg c\right) \wedge \left(c \vee \neg a \vee \neg b\right) \wedge \left(c \vee \neg b \vee \neg d\right)$$ 
    (b∨(¬a)∨(¬c))∧(c∨(¬a)∨(¬b))∧(c∨(¬b)∨(¬d))
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